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\frac{\left(x-4\right)\left(x+2\right)}{\left(x-1\right)\left(x+2\right)}-\frac{6}{x-1}
Factor the expressions that are not already factored in \frac{x^{2}-2x-8}{x^{2}+x-2}.
\frac{x-4}{x-1}-\frac{6}{x-1}
Cancel out x+2 in both numerator and denominator.
\frac{x-4-6}{x-1}
Since \frac{x-4}{x-1} and \frac{6}{x-1} have the same denominator, subtract them by subtracting their numerators.
\frac{x-10}{x-1}
Combine like terms in x-4-6.
\frac{\left(x-4\right)\left(x+2\right)}{\left(x-1\right)\left(x+2\right)}-\frac{6}{x-1}
Factor the expressions that are not already factored in \frac{x^{2}-2x-8}{x^{2}+x-2}.
\frac{x-4}{x-1}-\frac{6}{x-1}
Cancel out x+2 in both numerator and denominator.
\frac{x-4-6}{x-1}
Since \frac{x-4}{x-1} and \frac{6}{x-1} have the same denominator, subtract them by subtracting their numerators.
\frac{x-10}{x-1}
Combine like terms in x-4-6.